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具有营养循环和时滞的浮游生物系统的稳定性及Hopf分支

Stability and Hopf-bifurcations in a Delayed Nutrient Recycling Plankton System
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摘要 建立并研究了具有营养循环和时滞的浮游动植物模型,模型中描述浮游动植物间的相互作用函数是Holling-Ⅲ型功能反应函数.首先讨论了模型解的正性及有界性,然后分析了系统在无时滞和有时滞两种情况下边界平衡点和正平衡点的局部稳定性,并通过建立适当的Lyapunov函数,讨论了平衡点的全局稳定性.研究表明,随着时滞的增加,系统会出现Hopf分支. In this paper, a nutrient-toxin producing phytoplankon-zooplankton mathematical model with Holling Ⅲresponse function and time delay is proposed and analysed. The boundedness of solutions and the stability of the both boundary and positive equilibrium points for the system without delay as well as with delay are studied. Furthermore, by constructing suitable Lyapunov function, the global asymptotic stability of system is discussed. The results show that duo to the increase of the delay there occurs a Hopf bifurcation of periodic solutions.
作者 李晓娜 曼合布拜·热合木 LI Xiao-na;Mehbuba Rehim(College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, Chin)
出处 《数学的实践与认识》 北大核心 2018年第7期301-311,共11页 Mathematics in Practice and Theory
基金 国家自然科学基金(11261058)
关键词 Holling-Ⅲ型功能反应函数 时滞 稳定性 HOPF分支 营养循环 Holling type Ⅲ functional response delay stability Hopf bifurcation nutrientrecycling.
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